https://en.xen.wiki/index.php?action=history&feed=atom&title=31867edo 2026-06-29T11:01:45Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=31867edo&diff=205268&oldid=prev 2025-07-28T16:28:48Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:28, 28 July 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l9">Line 9:</td> <td colspan="2" class="diff-lineno">Line 9:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Harmonics in equal|31867}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Harmonics in equal|31867}}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Category:3-limit record edos]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Category:3-limit record edos<ins style="font-weight: bold; text-decoration: none;">|#####</ins>]] <ins style="font-weight: bold; text-decoration: none;">&lt;!-- 5-digit number --&gt;</ins></div></td></tr> </table>

FloraC https://en.xen.wiki/index.php?title=31867edo&diff=205265&oldid=prev 2025-07-28T16:27:05Z

<p>Cleanup &amp; + category</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:27, 28 July 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2">Line 2:</td> <td colspan="2" class="diff-lineno">Line 2:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{ED intro}} It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039{{c}} compressed.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{ED intro}} It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039{{c}} compressed.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">== Theory ==</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>31867edo inherits its mapping for the <ins style="font-weight: bold; text-decoration: none;">prime [[</ins>11<ins style="font-weight: bold; text-decoration: none;">/1|11]] </ins>from [[2897edo]], which is the only mapping shared between the two <ins style="font-weight: bold; text-decoration: none;">edo </ins>systems <ins style="font-weight: bold; text-decoration: none;">– </ins>unfortunately, this means that the <ins style="font-weight: bold; text-decoration: none;">prime </ins>11 is not good for stacking in this system. However, despite this, 31867edo is [[consistent]] through the [[21-odd-limit]]<ins style="font-weight: bold; text-decoration: none;">. </ins></div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>31867edo inherits its mapping for the 11<del style="font-weight: bold; text-decoration: none;">-prime </del>from [[2897edo]], which is the only mapping shared between the two <del style="font-weight: bold; text-decoration: none;">EDO </del>systems<del style="font-weight: bold; text-decoration: none;">- </del>unfortunately<del style="font-weight: bold; text-decoration: none;">, however</del>, this means that the 11<del style="font-weight: bold; text-decoration: none;">-prime </del>is not good for stacking in this system. <del style="font-weight: bold; text-decoration: none;"> </del>However, despite this, 31867edo is [[consistent]] through the [[21-odd-limit]], tempering out {{monzo| 305 -106 -59 }} and {{monzo| -122 285 -142 }} in the 5-limit; {{monzo| -7 30 -9 -7 }}, {{monzo| 51 -13 -1 -10 }}, and {{monzo| -8 2 -62 53 }} in the 7-limit; 6576668672/6576582375, 13841287201/13841203200, 11816941917501/11816406250000, and 28247524900000/28245855390489 in the 11-limit; [[123201/123200]], 1990656/1990625, 72773428/72772425, 1977326743/1977300000, and 6866455078125/6866343676192 in the 13-limit; 194481/194480, 336141/336140, 2000033/2000000, 9765888/9765625, 58464700/58461513, and 114244000/114243723 in the 17-limit; 89376/89375, 104976/104975, 165376/165375, 633556/633555, 709632/709631, and 742586/742577 in the 19-limit.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">As an equal temperament</ins>, <ins style="font-weight: bold; text-decoration: none;">31867et [[</ins>tempering out<ins style="font-weight: bold; text-decoration: none;">|tempers out]] </ins>{{monzo| 305 -106 -59 }} and {{monzo| -122 285 -142 }} in the 5-limit; {{monzo| -7 30 -9 -7 }}, {{monzo| 51 -13 -1 -10 }}, and {{monzo| -8 2 -62 53 }} in the 7-limit; 6576668672/6576582375, 13841287201/13841203200, 11816941917501/11816406250000, and 28247524900000/28245855390489 in the 11-limit; [[123201/123200]], 1990656/1990625, 72773428/72772425, 1977326743/1977300000, and 6866455078125/6866343676192 in the 13-limit; 194481/194480, 336141/336140, 2000033/2000000, 9765888/9765625, 58464700/58461513, and 114244000/114243723 in the 17-limit; 89376/89375, 104976/104975, 165376/165375, 633556/633555, 709632/709631, and 742586/742577 in the 19-limit.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Prime harmonics ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Prime harmonics ===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Harmonics in equal|31867}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Harmonics in equal|31867}}</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:3-limit record edos]]</ins></div></td></tr> </table>

FloraC https://en.xen.wiki/index.php?title=31867edo&diff=181892&oldid=prev 2025-02-20T16:33:28Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:33, 20 February 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Infobox ET}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Infobox ET}}</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{<del style="font-weight: bold; text-decoration: none;">EDO </del>intro<del style="font-weight: bold; text-decoration: none;">|31867</del>}} It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 <del style="font-weight: bold; text-decoration: none;">cents </del>compressed.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{<ins style="font-weight: bold; text-decoration: none;">ED </ins>intro}} It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039<ins style="font-weight: bold; text-decoration: none;">{{c}} </ins>compressed.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Theory ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Theory ==</div></td></tr> </table>

ArrowHead294 https://en.xen.wiki/index.php?title=31867edo&diff=128901&oldid=prev 2023-12-12T02:11:31Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 02:11, 12 December 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2">Line 2:</td> <td colspan="2" class="diff-lineno">Line 2:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EDO intro|31867}} It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EDO intro|31867}} It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>31867edo is [[consistent]] through the [[21-odd-limit]], tempering out {{monzo| 305 -106 -59 }} and {{monzo| -122 285 -142 }} in the 5-limit; {{monzo| -7 30 -9 -7 }}, {{monzo| 51 -13 -1 -10 }}, and {{monzo| -8 2 -62 53 }} in the 7-limit; 6576668672/6576582375, 13841287201/13841203200, 11816941917501/11816406250000, and 28247524900000/28245855390489 in the 11-limit; [[123201/123200]], 1990656/1990625, 72773428/72772425, 1977326743/1977300000, and 6866455078125/6866343676192 in the 13-limit; 194481/194480, 336141/336140, 2000033/2000000, 9765888/9765625, 58464700/58461513, and 114244000/114243723 in the 17-limit; 89376/89375, 104976/104975, 165376/165375, 633556/633555, 709632/709631, and 742586/742577 in the 19-limit.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== Theory ==</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">31867edo inherits its mapping for the 11-prime from [[2897edo]], which is the only mapping shared between the two EDO systems- unfortunately, however, this means that the 11-prime is not good for stacking in this system.  However, despite this, </ins>31867edo is [[consistent]] through the [[21-odd-limit]], tempering out {{monzo| 305 -106 -59 }} and {{monzo| -122 285 -142 }} in the 5-limit; {{monzo| -7 30 -9 -7 }}, {{monzo| 51 -13 -1 -10 }}, and {{monzo| -8 2 -62 53 }} in the 7-limit; 6576668672/6576582375, 13841287201/13841203200, 11816941917501/11816406250000, and 28247524900000/28245855390489 in the 11-limit; [[123201/123200]], 1990656/1990625, 72773428/72772425, 1977326743/1977300000, and 6866455078125/6866343676192 in the 13-limit; 194481/194480, 336141/336140, 2000033/2000000, 9765888/9765625, 58464700/58461513, and 114244000/114243723 in the 17-limit; 89376/89375, 104976/104975, 165376/165375, 633556/633555, 709632/709631, and 742586/742577 in the 19-limit.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Prime harmonics ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Prime harmonics ===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Harmonics in equal|31867}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Harmonics in equal|31867}}</div></td></tr> </table>

Aura https://en.xen.wiki/index.php?title=31867edo&diff=119731&oldid=prev 2023-07-09T07:16:28Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:16, 9 July 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">{{novelty}}{{stub}}</del>{{Infobox ET}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{Infobox ET}}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EDO intro|31867}} It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EDO intro|31867}} It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> </table>

BudjarnLambeth https://en.xen.wiki/index.php?title=31867edo&diff=119247&oldid=prev 2023-07-09T04:09:05Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 04:09, 9 July 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{Infobox ET}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{novelty}}{{stub}}</ins>{{Infobox ET}}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EDO intro|31867}} It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EDO intro|31867}} It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> </table>

BudjarnLambeth https://en.xen.wiki/index.php?title=31867edo&diff=102805&oldid=prev 2023-02-14T10:53:05Z

<p>Cleanup and improve intro</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:53, 14 February 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Infobox ET}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Infobox ET}}</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{EDO intro|31867}} It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed.</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">The '''</del>31867edo<del style="font-weight: bold; text-decoration: none;">''' divides the octave into 31867 equal parts of 0.03765651 cents each. It </del>is <del style="font-weight: bold; text-decoration: none;">the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past </del>[[<del style="font-weight: bold; text-decoration: none;">15601edo|15601]</del>]<del style="font-weight: bold; text-decoration: none;">, before [[79335edo|79335</del>]<del style="font-weight: bold; text-decoration: none;">], and has a fifth which is about 0.00000039 cents compressed.</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>31867edo is [[<ins style="font-weight: bold; text-decoration: none;">consistent</ins>]] through the [[21-odd-limit]], tempering out <ins style="font-weight: bold; text-decoration: none;">{{monzo</ins>| 305 -106 -59 <ins style="font-weight: bold; text-decoration: none;">}} </ins>and <ins style="font-weight: bold; text-decoration: none;">{{monzo</ins>| -122 285 -142 <ins style="font-weight: bold; text-decoration: none;">}} </ins>in the 5-limit; <ins style="font-weight: bold; text-decoration: none;">{{monzo</ins>| -7 30 -9 -7 <ins style="font-weight: bold; text-decoration: none;">}}</ins>, <ins style="font-weight: bold; text-decoration: none;">{{monzo</ins>| 51 -13 -1 -10 <ins style="font-weight: bold; text-decoration: none;">}}</ins>, and <ins style="font-weight: bold; text-decoration: none;">{{monzo</ins>| -8 2 -62 53 <ins style="font-weight: bold; text-decoration: none;">}} </ins>in the 7-limit; 6576668672/6576582375, 13841287201/13841203200, 11816941917501/11816406250000, and 28247524900000/28245855390489 in the 11-limit; [[123201/123200]], 1990656/1990625, 72773428/72772425, 1977326743/1977300000, and 6866455078125/6866343676192 in the 13-limit; 194481/194480, 336141/336140, 2000033/2000000, 9765888/9765625, 58464700/58461513, and 114244000/114243723 in the 17-limit; 89376/89375, 104976/104975, 165376/165375, 633556/633555, 709632/709631, and 742586/742577 in the 19-limit.</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">== Theory ==</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">31867edo is consistent </del>through the [[21-odd-<del style="font-weight: bold; text-decoration: none;">limit|21-odd </del>limit]], tempering out |305 -106 -59<del style="font-weight: bold; text-decoration: none;">&amp;gt; </del>and |-122 285 -142<del style="font-weight: bold; text-decoration: none;">&amp;gt; </del>in the 5-limit; |-7 30 -9 -7<del style="font-weight: bold; text-decoration: none;">&amp;gt;</del>, |51 -13 -1 -10<del style="font-weight: bold; text-decoration: none;">&amp;gt;</del>, and |-8 2 -62 53<del style="font-weight: bold; text-decoration: none;">&amp;gt; </del>in the 7-limit; 6576668672/6576582375, 13841287201/13841203200, 11816941917501/11816406250000, and 28247524900000/28245855390489 in the 11-limit; [[123201/123200]], 1990656/1990625, 72773428/72772425, 1977326743/1977300000, and 6866455078125/6866343676192 in the 13-limit; 194481/194480, 336141/336140, 2000033/2000000, 9765888/9765625, 58464700/58461513, and 114244000/114243723 in the 17-limit; 89376/89375, 104976/104975, 165376/165375, 633556/633555, 709632/709631, and 742586/742577 in the 19-limit.</div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">=== Prime harmonics ===</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Harmonics in equal|31867}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Harmonics in equal|31867}}</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">[[Category:Equal divisions of the octave|#####]] &lt;!-- 5-digit number --&gt;</del></div></td><td colspan="2" class="diff-side-added"></td></tr> </table>

FloraC https://en.xen.wiki/index.php?title=31867edo&diff=100285&oldid=prev 2022-12-22T10:25:42Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:25, 22 December 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Infobox ET}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Infobox ET}}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The '''<del style="font-weight: bold; text-decoration: none;">31867 edo</del>''' divides the octave into 31867 equal parts of 0.03765651 cents each. It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The '''<ins style="font-weight: bold; text-decoration: none;">31867edo</ins>''' divides the octave into 31867 equal parts of 0.03765651 cents each. It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Theory ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Theory ==</div></td></tr> </table>

Aura https://en.xen.wiki/index.php?title=31867edo&diff=100284&oldid=prev 2022-12-22T10:20:10Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:20, 22 December 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Infobox ET}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Infobox ET}}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The '''31867 edo''' divides the octave into 31867 equal parts of 0.03765651 cents each. It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed. 31867edo is consistent through the [[21-odd-limit|21-odd limit]], tempering out |305 -106 -59&amp;gt; and |-122 285 -142&amp;gt; in the 5-limit; |-7 30 -9 -7&amp;gt;, |51 -13 -1 -10&amp;gt;, and |-8 2 -62 53&amp;gt; in the 7-limit; 6576668672/6576582375, 13841287201/13841203200, 11816941917501/11816406250000, and 28247524900000/28245855390489 in the 11-limit; [[123201/123200]], 1990656/1990625, 72773428/72772425, 1977326743/1977300000, and 6866455078125/6866343676192 in the 13-limit; 194481/194480, 336141/336140, 2000033/2000000, 9765888/9765625, 58464700/58461513, and 114244000/114243723 in the 17-limit; 89376/89375, 104976/104975, 165376/165375, 633556/633555, 709632/709631, and 742586/742577 in the 19-limit.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The '''31867 edo''' divides the octave into 31867 equal parts of 0.03765651 cents each. It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== Theory ==</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>31867edo is consistent through the [[21-odd-limit|21-odd limit]], tempering out |305 -106 -59&amp;gt; and |-122 285 -142&amp;gt; in the 5-limit; |-7 30 -9 -7&amp;gt;, |51 -13 -1 -10&amp;gt;, and |-8 2 -62 53&amp;gt; in the 7-limit; 6576668672/6576582375, 13841287201/13841203200, 11816941917501/11816406250000, and 28247524900000/28245855390489 in the 11-limit; [[123201/123200]], 1990656/1990625, 72773428/72772425, 1977326743/1977300000, and 6866455078125/6866343676192 in the 13-limit; 194481/194480, 336141/336140, 2000033/2000000, 9765888/9765625, 58464700/58461513, and 114244000/114243723 in the 17-limit; 89376/89375, 104976/104975, 165376/165375, 633556/633555, 709632/709631, and 742586/742577 in the 19-limit.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{Harmonics in equal|31867}}</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Equal divisions of the octave|#####]] &lt;!-- 5-digit number --&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Equal divisions of the octave|#####]] &lt;!-- 5-digit number --&gt;</div></td></tr> </table>

Aura https://en.xen.wiki/index.php?title=31867edo&diff=96148&oldid=prev 2022-10-04T18:12:43Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:12, 4 October 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{Infobox ET}}</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The &#039;&#039;&#039;31867 edo&#039;&#039;&#039; divides the octave into 31867 equal parts of 0.03765651 cents each. It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed. 31867edo is consistent through the [[21-odd-limit|21-odd limit]], tempering out |305 -106 -59&amp;gt; and |-122 285 -142&amp;gt; in the 5-limit; |-7 30 -9 -7&amp;gt;, |51 -13 -1 -10&amp;gt;, and |-8 2 -62 53&amp;gt; in the 7-limit; 6576668672/6576582375, 13841287201/13841203200, 11816941917501/11816406250000, and 28247524900000/28245855390489 in the 11-limit; [[123201/123200]], 1990656/1990625, 72773428/72772425, 1977326743/1977300000, and 6866455078125/6866343676192 in the 13-limit; 194481/194480, 336141/336140, 2000033/2000000, 9765888/9765625, 58464700/58461513, and 114244000/114243723 in the 17-limit; 89376/89375, 104976/104975, 165376/165375, 633556/633555, 709632/709631, and 742586/742577 in the 19-limit.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The &#039;&#039;&#039;31867 edo&#039;&#039;&#039; divides the octave into 31867 equal parts of 0.03765651 cents each. It is the denominator of the next convergent for log&lt;sub&gt;2&lt;/sub&gt;3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed. 31867edo is consistent through the [[21-odd-limit|21-odd limit]], tempering out |305 -106 -59&amp;gt; and |-122 285 -142&amp;gt; in the 5-limit; |-7 30 -9 -7&amp;gt;, |51 -13 -1 -10&amp;gt;, and |-8 2 -62 53&amp;gt; in the 7-limit; 6576668672/6576582375, 13841287201/13841203200, 11816941917501/11816406250000, and 28247524900000/28245855390489 in the 11-limit; [[123201/123200]], 1990656/1990625, 72773428/72772425, 1977326743/1977300000, and 6866455078125/6866343676192 in the 13-limit; 194481/194480, 336141/336140, 2000033/2000000, 9765888/9765625, 58464700/58461513, and 114244000/114243723 in the 17-limit; 89376/89375, 104976/104975, 165376/165375, 633556/633555, 709632/709631, and 742586/742577 in the 19-limit.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Equal divisions of the octave|#####]] &lt;!-- 5-digit number --&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Equal divisions of the octave|#####]] &lt;!-- 5-digit number --&gt;</div></td></tr> </table>

Aura